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Simplifying 4a2 + -94a + 432 = 0 Reorder the terms: 432 + -94a + 4a2 = 0 Solving 432 + -94a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(216 + -47a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(216 + -47a + 2a2)' equal to zero and attempt to solve: Simplifying 216 + -47a + 2a2 = 0 Solving 216 + -47a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 108 + -23.5a + a2 = 0 Move the constant term to the right: Add '-108' to each side of the equation. 108 + -23.5a + -108 + a2 = 0 + -108 Reorder the terms: 108 + -108 + -23.5a + a2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + -23.5a + a2 = 0 + -108 -23.5a + a2 = 0 + -108 Combine like terms: 0 + -108 = -108 -23.5a + a2 = -108 The a term is -23.5a. Take half its coefficient (-11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. -23.5a + 138.0625 + a2 = -108 + 138.0625 Reorder the terms: 138.0625 + -23.5a + a2 = -108 + 138.0625 Combine like terms: -108 + 138.0625 = 30.0625 138.0625 + -23.5a + a2 = 30.0625 Factor a perfect square on the left side: (a + -11.75)(a + -11.75) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (a + -11.75) equal to 5.48292805 and -5.48292805.Subproblem 1
a + -11.75 = 5.48292805 Simplifying a + -11.75 = 5.48292805 Reorder the terms: -11.75 + a = 5.48292805 Solving -11.75 + a = 5.48292805 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + a = 5.48292805 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + a = 5.48292805 + 11.75 a = 5.48292805 + 11.75 Combine like terms: 5.48292805 + 11.75 = 17.23292805 a = 17.23292805 Simplifying a = 17.23292805Subproblem 2
a + -11.75 = -5.48292805 Simplifying a + -11.75 = -5.48292805 Reorder the terms: -11.75 + a = -5.48292805 Solving -11.75 + a = -5.48292805 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + a = -5.48292805 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + a = -5.48292805 + 11.75 a = -5.48292805 + 11.75 Combine like terms: -5.48292805 + 11.75 = 6.26707195 a = 6.26707195 Simplifying a = 6.26707195Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.23292805, 6.26707195}Solution
a = {17.23292805, 6.26707195}
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